Solve not working with cross product with units

I recently asked this question about using Solve with cross product.Solve not working when doing cross-productWhen I use the units in the definition of the variables, I am not able to get an answer.

x = Quantity[{1, 0, 0}, "Meters"];z = Quantity[{0, 0, 1}, "Newtons"*"Meters"]; Solve[z == Cross[x, y], y \[Element] FullRegion[3]]

The output is just:

Thanks for your help!