Olympiad Geometry · Challenge problem

Segments $\overline{AC}$ and $\overline{BD}$ bisect each other at point $E$, so $\triangle AEB \cong \triangle CED$ by SAS (vertical angles at $E$ plus the bisected segments). If $AB = 3x - 5$ and $CD = 19$, while $AE = 2y + 1$ and $EC = 15$, find $x + y$.