2018 AMC 12B Problem #12

Side $\overline{AB}$ of $\triangle ABC$ has length 10. The bisector of angle $A$ meets $\overline{BC}$ at $D,$ and $CD = 3.$ The set of all possible values of $AC$ is an open interval $(m,n).$ What is $m + n$ ?

This problem is part of the 2018 AMC 12B .