How to find the polynomial which has the sum of two cube roots as one of its roots?

Question

For example. How do I find the polynomial which has $\sqrt[3]2 + \sqrt[3]3$ as one of its roots?

( Hint: polynomial is $x^9-15x^6-87x^3-125$ )

Answer 1

$$A=\sqrt[3]3+\sqrt[3]2\implies A^3=3+2+3\sqrt[3]6(A)\implies A^3-5=3A\sqrt[3]6$$

Now cube both sides