10.1. Solve the equation $\left(x^{4}+x+1\right)(\sqrt[3]{80}-\sqrt[3]{0.01})=2(\sqrt[3]{5.12}+\sqrt[3]{0.03375})$.
Answer: $x_{1}=0, x_{2}=-1$. Solution. Multiply both sides of the equation by $\sqrt[3]{100}$, we get $\left(x^{4}+x+1\right)(\sqrt[3]{8000}-\sqrt[3]{1})=2(\sqrt[3]{512}+\sqrt[3]{3.375}) \Leftrightarrow 19 \cdot\left(x^{4}+x+1\right)=2(8+1.5) \Leftrightarrow x^{4}+x+1=1 \Leftrightarrow$ $x\left(x^{3}+1\right)=0$. Therefore, $x_{1}=0, x_{2}=-1$.