#### Answer

$x=-1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\sqrt[3]{6x+2}-\sqrt[3]{4x}=0
,$ transpose the second term and then raise both sides to the third power. Then isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{6x+2}=\sqrt[3]{4x}
.\end{array}
Raising both sides to the third power, the given equation is equivalent to
\begin{array}{l}\require{cancel}
6x+2=4x
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
6x-4x=-2
\\\\
2x=-2
\\\\
x=-\dfrac{2}{2}
\\\\
x=-1
.\end{array}