Hmm, that is very interesting. I'm fairly good at imagining stuff but not to the point of e.g. looking at Rubik's cube and then solving it blind.

I have a theory here. The mental imagery requires two things:

A: forming mental image somewhere in your brain - akin to how Boeing will simulate aircraft in computer. B: perceiving it consciously.
Some people might lack B but possess some form of A which they could not consciously access. I'm pretty sure that A can work without B in myself - e.g. good mechanical design can just pop in my mind, the kind of good mechanical design that absolutely requires some sort of simulation to produce. Yet I did not consciously imagine variations of that design.

The most important part of A for me is ability to imagine system and the rules and evolution of that system. For example I can even imagine configuration of conductors, and then imagine electric potential and electric field around them, from just the differential equations (i simply know how nabla squared times a looks). I can do that in 3D, and i imagine the 3D itself, not the 2D projection (which i can imagine if i need to). It's a lot like imagining soap film surface (it obeys same equations).