Given the information offered the only way to arrive at an answer is (as mentioned in the comments) to experiment with different weights and see what works.
Big Bang Method
If over loading the cabinet will not cause a catastrophic event - hurting someone or damaging something you care about - you could load a large amount of weight and then periodically ...
As mentioned above solid lumber can be had in long lengths, also plywood can be had in in longer lengths a 12' would be difficult and expensive to get. Turn a problem into a feature use an 8' piece with 2' cross grain (bread broad like) on the ends.