\displaystyle\lim_{x\to +\infty}\frac{1}{x^2-x\sqrt[3]{1-x^3}+(\sqrt[3]{1-x^3})^2}=\\
=\displaystyle\lim_{x\to +\infty}\frac{1}{x^2}\cdot\displaystyle\lim_{x\to +\infty}\frac{1}{1-\sqrt[3]{x^{-3}-1}+(\sqrt[3]{x^{-3}-1})^2}=0\cdot\frac{1}{3}=0