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What about iterating z = z - n z^(n-1) / (z^n - 1) and plotting a voxel if z^n is substantially different from (1,0,0) after 20-30 iterations or so?

Convergence seems quite slow so you may need more iterations, but it also looks quite chaotic from some quick numeric experiments.  It looks like the only three roots are the usual complex ones, but you do have points that converge outside the xy plane (e.g. 0.2,0.2,2 diverges, but 0.2,0.2,2.4 diverges).

You need some care because Newton's method does not converge always, for example applying the iteration to (0,0,1) divides by zero instantly.