HMMT November 2015 E6

Consider all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ satisfying

$$f(f(x)+2 x+20)=15$$

Call an integer $n$ good if $f(n)$ can take any integer value. In other words, if we fix $n$, for any integer $m$, there exists a function $f$ such that $f(n)=m$. Find the sum of all good integers $x$.