Answer
The solution is $j=1$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt[3]{7j-2}=\sqrt[3]{j+4}$
Cube each side of the equation.
$\Rightarrow (\sqrt[3]{7j-2})^3=(\sqrt[3]{j+4})^3$
Simplify.
$\Rightarrow 7j-2=j+4$
Add $2-j$ to each side.
$\Rightarrow 7j-2+2-j=j+4+2-j$
Simplify.
$\Rightarrow 6j=6$
Divide each side by $6$.
$\Rightarrow j=1$
Check $j=1$.
$\Rightarrow \sqrt[3]{7j-2}=\sqrt[3]{j+4}$
$\Rightarrow \sqrt[3]{7(1)-2}=\sqrt[3]{1+4}$
$\Rightarrow \sqrt[3]{7-2}=\sqrt[3]{1+4}$
$\Rightarrow \sqrt[3]{5}=\sqrt[3]{5}$
True.
Hence, the solution is $j=1$.
