Answer
$x=-126$
Work Step by Step
Raising both sides to the third power and isolating the variable, the given equation is equivalent to
\begin{array}{l}\require{cancel}
(x+1)^{1/3}=-5
\\\\
\left[(x+1)^{1/3}\right]^3=(-5)^3
\\\\
x+1=-125
\\\\
x=-125-1
\\\\
x=-126
.\end{array}
Upon checking, $
x=-126
$ satisfies the original equation.
