Cube roots equation

Algebra Level 5

15x13+13x+13=4x3\large\sqrt[3]{15x-1}+\sqrt[3]{13x+1}=4\sqrt[3]{x}

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

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

Clarification: x3=x3 \sqrt[3]{-x} = -\sqrt[3]{x} for all real xx.

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