Answer
$x=1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\sqrt[3]{-6x-1}=\sqrt[3]{-2x-5}
,$ raise both sides to the exponent equal to the index of the radical. Then use the properties of equality to isolate the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Get rid of the radical symbol by raising both sides of the equation above to the exponent equal to $
3
$ (the same index as the radical). This results to
\begin{array}{l}\require{cancel}
(\sqrt[3]{-6x-1})^3=(\sqrt[3]{-2x-5})^3
\\\\
-6x-1=-2x-5
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
-6x+2x=-5+1
\\\\
-4x=-4
\\\\
x=\dfrac{-4}{-4}
\\\\
x=1
.\end{array}
Upon checking, $
x=1
$ satisfies the original equation.