The equation of the perpendicular bisector of the line segment joining the points \((-3,8)\) and \((-5,4)\) is \(y = mx + b\). 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 \(\overline{AB}\).