Rationalizing an expression with different nth-roots in the denominator

Question

I was trying to help a friend of mine rationalize the following expression:

$$\frac{b}{\sqrt[3]{a^4}-\sqrt[3]{c^2}} $$

Simply multiplying by the conjugate won't work, even with multiple iterations.

Is there any way to solve this (even with some specific/advanced/obscure method) ? Or the expression isn't rationalizable? Maybe some polynomial method?

Thanks all

Answer 1

HINT: Try using the fact that

$$(x-y)(x^2+xy+y^2) = x^3 - y^3$$

...in particular, when $x=a^{4/3}$ and $y=c^{2/3}$.