# Cube roots equation

Algebra Level 5

$\large\sqrt[3]{15x-1}+\sqrt[3]{13x+1}=4\sqrt[3]{x}$

If the sum of all real roots $x$ that satisfy the equation above can be expressed as $- \dfrac{a}b$, where $a$ and $b$ are coprime positive integers, find $a+b$.

If you think that no solution exists, submit your answer as 666.

Clarification: $\sqrt[3]{-x} = -\sqrt[3]{x}$ for all real $x$.

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