\[\sqrt[3]{x\sqrt[5]{x}} = \sqrt[3]{\sqrt[5]{x^{5}} \cdot \sqrt[5]{x}} =\]
\[= \sqrt[3]{\sqrt[5]{x^{5} \cdot x}} = \sqrt[3]{\sqrt[5]{x^{6}}} =\]
\[= \sqrt[15]{x^{6}} = \sqrt[5]{x^{2}}\]
\[x = \sqrt{6^{5}}:\]
\[\sqrt[5]{\left( \sqrt{6^{5}} \right)^{2}} = \sqrt[6]{6^{5}} = 6.\]