Consider all functions $f:\mathbb{Z}\to\mathbb{Z}$ satisfying $$f(f(x)+2x+20)=15$$ Call an integer $n$ $\textit{good}$ 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 $x$.