Answer
$-7$.
Work Step by Step
The given functions are
$f(x)=(5x+16)^{\frac{1}{3}}$ and $g(x)=(x-12)^{\frac{1}{3}}$
Equate both functions
$\Rightarrow f(x)=g(x)$
$\Rightarrow (5x+16)^{\frac{1}{3}}=(x-12)^{\frac{1}{3}}$
Cube both sides.
$\Rightarrow \left [(5x+16)^{\frac{1}{3}}\right ]^3=\left [(x-12)^{\frac{1}{3}}\right ]^3$
Multiply exponents on both sides.
$\Rightarrow 5x+16=x-12$
Add $-x-16$ to both sides.
$\Rightarrow 5x+16-x-16=x-12-x-16$
Simplify.
$\Rightarrow 4x=-28$
Divide both sides by $4$.
$\Rightarrow \frac{4x}{4}=\frac{-28}{4}$
Simplify.
$\Rightarrow x=-7$.
