BD-BDMO 2021 Problem 3

Let $ABC$ be a triangle with incenter $I$ . Points $E$ and $F$ are on segments $AC$ and $BC$ respectively such that, $AE=AI$ and $BF=BI$ . If $EF$ is the perpendicular bisector of $CI$ , then $\angle{ACB}$ in degrees can be written as $\frac{m}{n}$ where $m$ and $n$ are co-prime positive integers. Find the value of $m+n$ .