# Something interesting in cubes

Algebra Level 4

$\large 8x^{3}-12x^{2}-6x-1=0$

If the value of a real root that satisfy the equation above can be expressed as

$\large \dfrac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}$

where $$a,b$$ and $$c$$ are positive integers, find the value of $$a+b+c$$.

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