\(2\sqrt[3]{3x-2}+3\sqrt{6-5x}-8=0\)
\(\Leftrightarrow\left(2\sqrt[3]{3x-2}+4\right)+\left(3\sqrt{6-5x}-12\right)=0\)
\(\Leftrightarrow2\dfrac{3x-2+8}{\sqrt[3]{\left(3x-2\right)^2}-\sqrt[3]{2\left(3x-2\right)}+\sqrt[3]{4}}+3\dfrac{6-5x-16}{\sqrt{6-5x}+4}=0\)
\(\Leftrightarrow\dfrac{6\left(x+2\right)}{\sqrt[3]{\left(3x-2\right)^2}-\sqrt[3]{2\left(3x-2\right)}+\sqrt[3]{4}}+\dfrac{-15\left(x+2\right)}{\sqrt{6-5x}+4}=0\)
\(\Leftrightarrow\left(x+2\right)\left(\dfrac{6}{\sqrt[3]{\left(3x-2\right)^2}-\sqrt[3]{2\left(3x-2\right)}+\sqrt[3]{4}}+\dfrac{-15}{\sqrt{6-5x}+4}\right)=0\)
\(\Rightarrow x+2=0\Rightarrow x=-2\)
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