output 3d{-1,1,1,1,1,2} named "fiveSixths"
Your mechanic returns 1 success exactly 5/6ths of the time. But it's a lumpy bi-modal distribution on 1 and 3.5 total successes. Make sure to provide free aspirin to players, as calculating results will be entailed.
There's a built-in explode function, but you have to use it before doing your other processing. Specifically, use FOOdBAR to have BAR evaluated as a sequence and used to generate FOO "dice" with arbitrary side counts and values. Here, DICEd([explode d6]) does the job, turning an exploded d6 into the base for the actual roll. (explode doesn't separate dice that you give it — you have to do that, or you'll get a 5d6 roll that only explodes, once, on 30.)
You can't compare sequences to a threshold to get a list or sum of values against that threshold — you'll just get the sequence summed and checked against the threshold. Instead, use [count VALUES in SEQUENCE] for each of the valid values (3-6). And as it turns out, since every 6 triggers a new die and all those dice count, you can just double-count 6s once exploded. So really that should be [count {3..6, 6} in ROLL].
The results, as best I can manage, aren't pretty. Each explosion will either fumble harder (1), make no progress against fumbling (2-5), or break even and get a new chance to do the same thing (6), and the more dice you start with, the more chances for explosions. There is no provision for fumbles to peter out in explosions, as one would expect from a great success; the only question is whether the chain ends with a 1 or not.
Best Answer
In a "dice pool," one considers each die individually, rather than as a collection of components to be summed. As an example, an attack in the HERO System might do 8d6 damage; to resolve it, you'd roll eight six-sided dice and add them up to produce a number between 8 and 48. In a die pool system, you might see how many of the dice showed a 5 or a 6 on the top face, and count those as "successes" toward a benchmark.
Rolling vs. a target number can be used in both die pool systems and otherwise. In HERO, for example, you roll 3d6 and sum them, trying to stay below 11 (or an otherwise modified target). In Deadlands, you use your die pool and select the highest rolled die, comparing it with a target number modified by the difficulty of the task at hand.