Submitted by devansh shringi

Algebra Level 4

A cubic polynomial

$f(x) = 8x^3-3x^2-3x-1$

has one real root of the form $\frac{ \sqrt[3]{a} + \sqrt[3]{b} + 1} { c}$ , where $a, b, c$ are positive integers. Find $a + b + c$ .