Find all integers $n$ such that there exists a polynomial $P(x)$ with integer coefficients satisfying $$P(\sqrt[3]{n^2} + \sqrt[3]{ n}) = 2016n + 20\sqrt[3]{n^2} + 16\sqrt[3]{n}$$
Source: 2016 Saudi Arabia BMO TST , level 4+, II p3
Tags: polynomial, Integer Polynomial
Find all integers $n$ such that there exists a polynomial $P(x)$ with integer coefficients satisfying $$P(\sqrt[3]{n^2} + \sqrt[3]{ n}) = 2016n + 20\sqrt[3]{n^2} + 16\sqrt[3]{n}$$