I have noticed that doing lvl 60 Dungeons calls for a PvP gear must have on you.
It's not like you can enter a Dungeon free handed.
There is some non PvP gear out there you might say, that can get you thru a Dungeon, but i say it is not enough.
As a Rogue that I choose to be i found out that if you have your PvP gear on you can go thru Dungeons no problem.
There is a big question on your mind of the Abillities that you should choose when you go inside a Dungeon? ; well then definitely you will not choose the same as you use in PvP because Dungeons are quite Different.
Anyway if you are to reach a Dungeon at a lower level it is possible to do it till the end.
If I am to consider the Dungeon - The Throne of Idris as a level 30 + (something), you can see that it can be done just by checking
this link here.