Real Root

Algebra Level 4

The real root of the equation \(8x^3 - 3x^2 - 3x - 1 = 0\) can be written in the form \(\dfrac{\sqrt[3]a + \sqrt[3]b + 1}{c}\), where \(a\), \(b\), and \(c\) are positive integers. Find \(a+b+c\).

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