The sum of the roots

Question

The function $f(x)$ has exactly six different roots, and is such that $f(11+x)=f(11-x)$. How do you find the sum of the roots ?

Answer 1

The condition implies that if $r$ is a root so is its reflection with respect to $11$. Thus the six roots can be organized into three pairs, each summing 22, and the sum of all six roots is 66.