Factorization is an art

Algebra Level 5

A root of 10x33x23x1=010x^3-3x^2-3x-1=0 is of the form a3+b3+1c\dfrac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}, where aa, bb, and cc are positive integers. Find a+b+ca+b+c.

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