Although movement in 5e is not governed by squares, they are probably a helpful model to this particular exercise. Everything in the universe is effectively measured in 5' increments and using squares to model this will give us an effective answer to this question Let's posit a 50' wall
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Now let's look at the veritcal space next to the wall
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Finally we need to have the flat part on top of the wall, and the space above that
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Now, supposing our hero starts at the first y (marked a below), and runs up, he runs out of movement at the 10th y (marked b below).
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bxxxxxxxxx
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ax
If you start at a, you might be able to climb up onto the top of the wall. However, if you have a 45 foot wall you are safe. If you have to move to a, a dash would be required to not fall (as you don't have the ability to stay vertical).
The problem here is that if the wall extends at all into the square above the one marked b, then you're in trouble, you have to move into the square above it as diagonal movement is not possible.
This will be both at the discretion of the map makers (if the building extends a bit above the square you're probably not going to move diagonally) and also your DM (he may allow a bit of wiggle room here). Consult your DM before you attempt any 50' wall climbs.
45' wall climbs (and lower) are safe though.
Yes, it is possible but...
The number of ways you can go about it is limited to somehow seeing through magical darkness like by getting Truesight.
Or by picking up 2 levels of Warlock for the Devil's Sight Eldritch Invocation, in order for you to see through magical darkness up to 120 feet.
Or by any means like the 6th-level Divination Spell True Seeing, or a Gem of Seeing (page 172 of the DMG) also does the trick, or you can homebrew a magic item that serves this purpose.
What is important is that you can see the area of magical darkness/dim light created, all others might still see it as magical darkness, that doesn't matter.
However, the bottom line is that both of these features were not meant to provide a mini-portal for the monk to Shadow Step through because Shadow Step, by its wording:
Shadow Step
At 6th level, you gain the ability to step from one shadow into another. When you are in an area of dim light or darkness, as a Bonus Action you can teleport up to 60 feet to an unoccupied space you can see that is also in dim light or darkness...
Emphasis on shadow here, we can see that the intent was for the Monk to step through shadows, not magical darkness. I know this sounds silly but if we look at the next emphasis, "you can see", it affirms this intent by limiting the area a Monk can step through to an area he can see. Hence, these two were not meant to be used in-tandem due to its incompatible properties. However, there are many uses for Darkness and Shadow Step alone in themselves. Darkness can be used to Blind enemies, causing them to have Disadvantage on Attack Rolls. One clever trick is also to use Darkness to cover a room's light source like a single torch, Darkness negates that source and engulfs the whole room in natural darkness, giving any creature with Darkvision advantage. Shadow Step can enable the Monk to avoid stepping into a brightly-lit portion of a room (and thereby avoid being seen) by teleporting to a dimly-lit portion.
Don't misunderstand me, stepping through magical darkness can be done but you'll have to work for it
Best Answer
Yes, you can do this, with a caveat
The Way of Shadow monk's Shadow Step feature (PHB, p. 80) says:
The warlock's Devil's Sight eldritch invocation says:
The darkness spell says
Since your invocation is more specific than the general rule laid out in darkness, you are able to see into the darkness... though the invocation gives no benefits for merely dim light. See this other question/answer for more detail.
Your monk's ability works with any darkness you can see. Since you can see into this darkness, yes, you can Shadow Step in to your own magical darkness.
Is this broken? I don't think so. It requires you be at least an 8th-level character, and sacrifice a full 8-level progression in Way of Shadow monk in order to get 2 levels of warlock, which give you very little else that you're interested in. You also have to expend a spell slot to do it, and give up the extra attack(s) that you'd get from your bonus action as a monk.