\(\sqrt[3]{x+2}+\sqrt[3]{7-x}=3\)
\(\Leftrightarrow x+2+7-x+3\sqrt[3]{x+2}.\sqrt[3]{7-x}\left(\sqrt[3]{x+2}+\sqrt[3]{7-x}\right)=27\)
\(\Rightarrow9+9\sqrt[3]{\left(x+2\right)\left(7-x\right)}=27\)
\(\Leftrightarrow\sqrt[3]{\left(x+2\right)\left(7-x\right)}=2\) \(\Leftrightarrow\left(x+2\right)\left(7-x\right)=8\) \(\Leftrightarrow x^2-5x-6=0\) \(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=6\end{matrix}\right.\) (thỏa mãn) Vậy phương trình có nghiệm là : \(x=-1\) và \(x=6\)