DragonKing: Given the choice I'd recommend without. Get a good understanding of chequer play first. Part of the use of the cube is to terminate games so that you don't risk the percentage of losses that exist at that point unless you opponent is willing to pay the price. Without the cube you'll be playing into those situations and thus learning about them.

I spent 12 or more months on chequer play alone before I took on the cube. It worked for me. Others who did both, well it'll have worked for them, too, lol. But I'd say the ASAP aspect precludes the cube. I'd imagine that overall progress will be slower if you're advancing on two fronts.