Factorization is an art (4)

Algebra Level 5

\[\large f(x)= x^3+21x^2+147x+336\] Let \(f: \mathbb {R \to R}\) be defined as above.

If the real root of the equation \( \underbrace{f(f(f(\dots f(f(x))\dots)))}_{2016\ \text{times}} =0\) is of the form \(\large -a+a^{1/ {3^b}} \), where \(a\) and \(b\) are integer, find \(a+b\).

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