## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=-126$
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.