To further illustrate how the magnetic sum of repulsion and attraction add up to zero ☝ here I intend to explain how the sum of north and south can be utilised in the same fashion.
Here the metal strip has become a magnet. It now has a northpole and a southpole.
This is that same strip and that same magnet, the only new thing is the additional second magnet. The metal strip now has a northpole at the right and a southpole at the left. The poles do-not extend all the way down the metal strip.
This effect is very easy to reproduce, and the lack of lifting power should be extremely evident.
The work done moving the second magnet away from the first is the same as the gain while moving towards it.
In this setup it should be easy to move the center magnet from left to right. The change in flux on the other hand is tremendous.