Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2}+\sqrt[3]{4}$ as a root.

I've been working on this question for some time, but I haven't made any headway. Can somebody write a solution to this?

Find a cubic polynomial with integer coefficients that has \( \sqrt[3]{2}+\sqrt[3]{4}\) as a root.

Answer see: https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1174265.html

The cubic polynomial is \(x^3-6x-6 = 0\)