$6.283 \frac{x \sqrt[5]{x}-1}{\sqrt[5]{x^{3}}-1}+\frac{\sqrt[5]{x^{3}}-1}{\sqrt[5]{x}-1}=16$
## Solution.

Let $y=\sqrt[5]{x}$, then $\frac{y^{6}-1}{y^{3}-1}+\frac{y^{3}-1}{y-1}=16 \Leftrightarrow y^{3}+y^{2}+y-14=0 \Leftrightarrow$ $\Leftrightarrow(y-2)\left(y^{2}+3 y+7\right)=0 \Leftrightarrow \sqrt[5]{x}=2 \Leftrightarrow x=32$.

Answer: $x=32$.