Answer
$x=4$
Work Step by Step
We are given:
$\sqrt[6]{2x+1}=\sqrt[6]{9}$
We raise both sides to the power of 6:
$(\sqrt[6]{2x+1})^{6}=(\sqrt[6]{9})^{6}
\\2x+1=9$
Subtract $1$ to both sides::
$2x=8$
Divide both sdies by $2$
$x=4$