\(\sqrt[3]{12-x}+\sqrt[3]{14+x}=2\)
\(\Leftrightarrow12-x+14+x+3\sqrt[3]{\left(12-x\right)\left(14+x\right)}\left(\sqrt[3]{12-x}+\sqrt[3]{14+x}\right)=8\)
\(\Leftrightarrow26+3\sqrt[3]{\left(12-x\right)\left(14+x\right)}.2=8\)
\(\Leftrightarrow\sqrt[3]{\left(12-x\right)\left(14+x\right)}=-3\)
\(\Leftrightarrow-x^2-2x+168=-27\)
\(\Leftrightarrow x^2+2x-195=0\)
\(\Leftrightarrow\left(x-13\right)\left(x+15\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=13\\x=-15\end{matrix}\right.\)
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