\[{\text{Найдите }}x \in \mathbb{N}.\] $$\frac{1}{{\sqrt[3]{{\cos \frac{{2\pi }}{9}}}}} + \frac{1}{{\sqrt[3]{{\cos \frac{{4\pi }}{9}}}}} + \frac{1}{{\sqrt[3]{{\cos \frac{{8\pi }}{9}}}}} = \sqrt[3]{{x\left( {\sqrt[3]{9} - 1} \right)}}$$