If science can't prove the existence of other dimensions forever Should I believe what is said in the Buddhist text instead? Even though I can't prove it myself either. 

http://www.accesstoinsight.org/ptf/dhamma/sagga/loka.html
Three possible approaches, here.

One, you just acceptt this on faith. Depending on your mindset, this can be something like believing the impossible or groundless, or something more like feeling like you need to a decision. You can't prove tea or coffee is better for breakfast, but you can't stand around all day weighting the alternatives. So you make a decision, aware that the reasoning has some holes.

Two, you look at these as a myth, an instructive story and you don't even put much thought into if the story is true. In our distant past, everything was hearsay. There was no science, no reliable news outlets, and it was just a bunch of people telling stories. People got used to some stories seeming a bit far fetched, but everyone you ever heard in your life was a bunch of plausible sounding stories.

Three, you look at these as patently incompatible with everything we know about the world from multiple reliable sources-- science, journalism, and so on. You either discard that part of Buddhism as nonsense, or alternatively review it and look for what can be salvaged-- for example, some modern readers view the cosmology as a metaphor for states of mind (hell is the state of mind in this world and this body that we put ourselves in when we act unskillfully)