Answer
$x= -32 $
Work Step by Step
Given \begin{equation}
\sqrt[3]{4 m+3}=-5.
\end{equation} First cube both sides to eliminate the radical signs (may be repeated), and solve for $m$.
\begin{equation}
\begin{aligned}
\sqrt[3]{4 m+3}&=-5\\
\left(\sqrt[3]{4 m+3}\right)^3&= \left( -5\right)^3\\
4 m+3& =-125\\
m&= \frac{-125-3}{4}\\
&=-32.
\end{aligned}
\end{equation} Check.
\begin{equation}
\begin{aligned}
\sqrt[3]{4 (-32)+3}&\stackrel{?}{=}-5\\
-5& =-5\quad \quad \textbf{True}.
\end{aligned}
\end{equation} The solution is $x= -32 $.
