Answer
$x=-\dfrac{2}{3}$
Work Step by Step
Raising both sides to the $\text{
third
}$ power, the solution of the given equation, $
\sqrt[3]{2x}=\sqrt[3]{5x+2}
,$
\begin{array}{l}\require{cancel}
2x=5x+2
\\\\
2x-5x=2
\\\\
-3x=2
\\\\
x=\dfrac{2}{-3}
\\\\
x=-\dfrac{2}{3}
.\end{array}