Refer to the figure: In right triangle $ABC$ with right angle at $C$, the base $AC$ is divided into segments of lengths 6 and 6 by a perpendicular from a point on $AB$ to $AC$. This perpendicular has length $x$, and the vertical leg $BC$ has length $y$. The area of triangle $ABC$ is at least 40 but no more than 80. If $y$ is an integer, what is the sum of all possible integer values of $x$?