#### Answer

$f^{-1}(x) = \frac{\sqrt[3] x - 5}{3}$

#### Work Step by Step

f(x) = $(3x + 5)^{3}$
y = $(3x + 5)^{3}$
Solve for x
$\sqrt[3] y = 3x + 5$
$\sqrt[3] y - 5 = 3x$
$\frac{\sqrt[3] y - 5}{3} = x$
Interchange x with y
$\frac{\sqrt[3] x - 5}{3} = y$
$\frac{\sqrt[3] x - 5}{3} = f^{-1}(x)$