I can still cut it entirely with the Loop cut.
Thing is, I want to get rid of that edge, I do that by dissolving it:
Now here's the problem, after that, I can't cut it entirely. I've also tried dissolving the remaining vertices but it didn't work.
So what I want to do is to cut it entirely after dissolving the edge, instead of doing it separately as you can see in the pic. Is there a way to achieve that? Did I make a wrong move?