#### Answer

$x=32$

#### Work Step by Step

Add 5 on both sides of the equation to obtain:
$\sqrt[3]{4x-3}=5$
RECALL:
For any real number $a$,
$(\sqrt[3]{a})^3=a$
Cube both sides then use the rule above to simplify:
$(\sqrt[3]{4x-3})^3 = 5^3
\\4x-3=125$
Add 3 on both sides to obtain:
$4x = 125+3
\\4x=128$
Divide 4 on both sides to obtain:
$x=\frac{128}{4}
\\x=32$