Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set - Page 453: 41

$x=1$

Raising both sides to the third power of the given equation, $ \sqrt[3]{-6x-1}=\sqrt[3]{-2x-5} ,$ then the solution/s is/are \begin{array}{l}\require{cancel} -6x-1=-2x-5 \\\\ -6x+2x=-5+1 \\\\ -4x=-4 \\\\ x=\dfrac{-4}{-4} \\\\ x=1 .\end{array}