algebra #1

Algebra Level 4

The equation \(2x^3-6x^2-12x-8=0\) has exactly one real root, which is in the form \(x=a+\sqrt[3]{b}+\sqrt[3]{c}\), where \(a\), \(b\) and \(c\) are positive integers.

Find \(a+b+c\).

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