Factorization is an art (4)

Algebra Level 5

f(x)=x3+21x2+147x+336\large f(x)= x^3+21x^2+147x+336 Let f:RRf: \mathbb {R \to R} be defined as above.

If the real root of the equation f(f(f(f(f(x)))))2016 times=0 \underbrace{f(f(f(\dots f(f(x))\dots)))}_{2016\ \text{times}} =0 is of the form a+a1/3b\large -a+a^{1/ {3^b}} , where aa and bb are integer, find a+ba+b.

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