10/11 hours a day is a long time for a dog to be alone with only one walk during this period. It may be boredom or may be separation anxiety. My dog walker will do 2 walks but charge me a reduced rate for the second walk. I use this if I have to work more than 6 hours as I don't like leaving her for that long. Crating is useful to stop dogs chewing and giving them a safe space, but I personally would never crate for that period of time.
I don't really feel very confident in giving advice but Inky (15months) has a crate. He goes in at night and when I'm out. When I get my work bag, or my coat that not for dog walking, he goes straight in on his own, ready for his tiny bit of crust! When I'm working he has one proper walk with the dog walker and another short visit from her. He always seems happy when I get in. I like the crate as I know he's safe and although he probably wouldn't chew now, I can't see the point in taking a risk. I think I read in Pippa's puppy hand book that it's us that view crates as a cage, why would a dog, to them it's just a bed.
Its awful to say this, but 10-11 hours is too long for your dog to be away from you. Dogs are pack animals, and they need stimulation from their pack or they turn to other ways to use their minds, like becoming a professional re-docorator in your house. I know that you want to have a dog, but maybe you are really a cat person. Or maybe your dog needs a friend.
I know a bit late on this for potential consideration depending on where you are at. All the advise has been good so far, we had something similar with ours at one stage where she would chew walls, sofa etc. There was no pattern that we could think off. Until one day I was at home and noticed next door neighbour makin a certain noise. This sent ours into a full out panic. Went and spoke to the neighbour and it was when he was moviing a pair of ladders that he just dragged along rather than carry. Hey presto carry ladders and everything is all OK. Just a thought that may be worth considering.