#### Answer

$x = 11$

#### Work Step by Step

Subtract 5 on both sides to obtain:
$(3x-6)^{\frac{1}{3}}=3$
Cube both sides to obtain:
$\left((3x-6)^{\frac{1}{3}}\right)^3=3^3
\\(3x-6)^{\frac{1}{3}(3)}=27
\\(3x-6)^1=27
\\3x-6=27$
Aadd 6 on both sides to obtain:
$3x=33$
Divide 3 on both sides to obtain:
$x = 11$