The perpendicular bisector of the line segment connecting the points $(-3,8)$ and $(-5,4)$ has an equation of the form $y = mx + b$. Find $m+b$.

Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{AB}$ and is perpendicular to $\overline{AB}$.