Any way to deal with this pair of cubics?

[Glen]

This relates to the post I made a while back on a nomogram for V = 12h³ −6ah² +ha²

I was playing with it just recently and got it into a form (with some constant factors removed, since they can be incorporated into the variables they multiply) like this:

(z/x)³ - 1 = [(y/x)-1]³

Which perhaps might have some way to be nomogrammable.

Does anyone see a way to do anything with that? Since we do have nomograms that solve cubics, I wondered if there might be something I wasn't seeing.