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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