Heh, I gave the earlier advice about going standby, assuming no one would be crazy enough to book a 6am flight! (So, never mind that...)

As others have said, 50-minute connections are doable at DEN, but as usual it does depend to some degree on how far you have to go. The terminal layout is simple enough, the weather in April is not likely to cause too much trouble, and even if there are short-lived weather problems at DEN the airport can recover fairly quickly. I would say that there's a very good chance you will make it.