I don't know, it depends on the place really, and the time of night. What is the atmosphere like? I'm not sure what you mean by scenarios - will it be a very adult place? Skating was my main hobby as a child and my sister and I used to be dropped off alone at night until 10.15pm, but it was at a club not a public session, where everyone knew us. Having said that, we often used to leave the premises to go to the nearby chip shop, with a group of friends and never asked our parents.
11 is quite young, and I have a ten year old son who is just beginning to seek independence, so I know how you feel. I don't think I would be happy for my son to do it unless it was very early in the evening, and even then I think I'd be inclined to hang about somewhere nearby until the end. But he is a whole year younger. Maybe it would be ok if you absolutely trusted your daughter to stay inside the rink and do nothing but skate until you collected her, but it's difficult to say.