#### Answer

$x=35$

#### Work Step by Step

Add 4 on both sides of the equation to obtain:
$\sqrt[3]{2x-6}=4$
RECALL:
For any real number $a$,
$(\sqrt[3]{a})^3=a$
Cube both sides then use the rule above to simplify:
$(\sqrt[3]{2x-6})^3 = 4^3
\\2x-6=64$
Add 6 on both sides to obtain:
$2x = 64+6
\\2x=70$
Divide 2 on both sides to obtain:
$x=35$