I was recently doing some translation of a text from Chinese to English, together with my wife, and I translated the following:
你也該努力看看，能不能稍稍改變
as:
you should do your best to see if you can't change things
My wife looked at it and suggested it should be can, not can't. When I looked at it again, I could find no way to explain why can't seems to be OK, and I could see no clear difference between the text above and:
you should do your best to see if you can change things
Given that this second version is more transparent, I decided to use it. But I find it bizarre that the sentence seems to mean the same thing whether it includes can or can't.
