#### Answer

$k=-4$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt[3]{2k-11}=\sqrt[3]{5k+1}
,$ raise both sides of the equation to the third power. Then use properties of equality to isolate and solve the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Raising both sides of the equation to the third power results to
\begin{array}{l}\require{cancel}
\left( \sqrt[3]{2k-11} \right)^3=\left( \sqrt[3]{5k+1} \right)^3
\\\\
2k-11=5k+1
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
2k-5k=1+11
\\\\
-3k=12
\\\\
k=\dfrac{12}{-3}
\\\\
k=-4
.\end{array}
Upon checking, $
k=-4
$ satisfies the original equation.