Answer
$x= 105.5 $
Work Step by Step
Given\begin{equation}
\sqrt[3]{2 x+5}=6.
\end{equation}Start by rewriting the radical as a power of fraction and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[3]{2 x+5}&=6\\
\left(2 x+5\right)^{\frac{1}{3}}&= 6\\
\left(\left(2 x+5\right)^{\frac{1}{3}}\right)^3& = \left( 6 \right)^3 \\
2x+5& =216\\
x&= \frac{216-5}{2}\\
& = 105.5.
\end{aligned}
\end{equation} Check.
\begin{equation}
\begin{aligned}
\left(2\cdot105.5+5\right)^{\frac{1}{3}}&\stackrel{?}{=}6 \\
6& =6\quad \checkmark.
\end{aligned}
\end{equation} The solution is $x= 105.5 $.
