But seriously, I think we can all agree that among the literary arts, poetry is the most likely to be accidentally uninterpretable. Due to its cultural context it is also the area where uninterpretability is the most likely to be accepted. This creates an environment where you run a serious risk of developing a culture of meaninglessness.
Some poetry is made to make you laugh like Billy Collins' Another Reason Why I Don't Keep A Gun in the House.
Some poetry is purposefully inscrutable and difficult because the author wants you to work to understand them. A good example of this might be r-p-o-p-h-e-s-s-a-g-r by E.E. Cummings.
Each of these examples is meaningful in its own different way. I think trying to decide what has meaning is hard because you might automatically discard a work of art that is "just for fun". Isn't play meaningful?
I am sure the same applies, to e.g. William Blake.