$\large f(x)= x^3+21x^2+147x+336$
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 $a+b$.