I have a few ideas...
How long is she in the crate? Are you free feeding her or feeding her on a schedule? Or how many times per day. At 11 months, twice a day is fine, and feeding twice a day typically means they poop twice a day. You should be feeding her and then immediately taking her out to go. Walk around the block, stand in the yard with her, whatever you need to do to MAKE SURE she goes before you put her in the crate. At that age, you only want to put an empty dog in the crate. Stand OUTSIDE with the treat. She may associate the treat with coming inside, not pooping.
I had a little "stinker" too! We got Sam at 10 months and it took FOREVER to get her to stop pooping in the closet. The bell helped, so she could let us know when she wanted to go out, but she would still sneak off. Basically it came down to standing on the porch and making sure she went twice a day and not letting her inside until she went. Now she's so proud of herself when she goes she does a little prance when she comes back to the door.
I would also give her a small treat, maybe in a puzzle toy like a Kong, when she is in the crate. You can also feed her in the crate so that she more closely associates it with her "home" so she doesn't poop in there. Make sure she's not in there longer than she can hold it and make sure she's empty when she goes in. It will get better. They all start to really catch on around 1 year old and most of them are trained (if you work hard at it!) by 18 months

It took us 6 months from when we got Sam to get her trained.