[TangoTrotFox]

You can't ignore the gravitational force of the normal mass. The two would rapidly reach a zero-value equilibrium at some point where the repulsive force of the negative mass is perfectly cancelled out by the attractive gravity of the positive mass, so you have a net force of 0 at some distance.

For an easier to visualize example imagine placing one magnet positive pole up inside of a tube, and then you place another magnet positive pole down in the same tube. It would create a similar effect. There is a repulsive force being perfectly balanced out by an attractive force and the two reach an equilibrium where the magnet on top is 'floating' with the net of all forces in this closed system being 0.