Answer
$x=-2$
Work Step by Step
Raising both sides to the $\text{
third
}$ power, the solution of the given equation, $
\sqrt[3]{4x+3}=\sqrt[3]{2x-1}
,$
\begin{array}{l}\require{cancel}
4x+3=2x-1
\\\\
4x-2x=-1-3
\\\\
2x=-4
\\\\
x=-\dfrac{4}{2}
\\\\
x=-2
.\end{array}