We've been through this with our kids. To be honest, I think it would be quite unusual for kids this age to happily skip off saying ' just going to do my music practice, Mum' ( although I guarantee that some MNer will now say their dd/ds does...)
I think it is a parent's responsibility to get them into good habits, remind, cajole, set reasonable goals, and reward effort.
I think 30 mins at this stage might be ambitious - why not start at 10 or 15 mins. It's the getting started that's the problem and we found that if we said he had to do at least 10 mins then he'd often play longer in the end anyway.
I know it sounds a bit silly for an 11 year old, but we found using a bag of reward tokens helped ( an idea I got from MN !) I printed out a sheet of 'tokens' which included things like 15 mins extra time on the Xbox / 10% of a £5 iTunes voucher ( collect 10 to redeem)/ friend over for a sleepover etc. I had about 30 - so about a months worth. Included were a couple of 'big' ones like 'a £20 Amazon voucher'. At the end of each month, if he'd practiced regularly then he would be guaranteed to get the big one, but if not he wouldn't necessarily, and I'd add all the little ones back into the bag for the next month!
I know it sounds mad, but it really worked! More bizarrely, my 13 yr old realised this was effectively a way of augmented his pocket money, so asked to join the scheme 
I came to the conclusion that if I was paying £15 week for a lesson, it was worth paying about £4 week to incentivise the practice!
Are you or your DH musical? it's also really important for kids to understand what is called 'purposeful practice' e.g. The difference between
- today I am going to do music practice, and
- today I am going to practice the first four bars of that song until I can play it without making any mistakes
Then it really helps them have a sense of achievement. So don't just say ' go and practice', say what are you going to achieve in this 15 min practice.
Does he play in any groups at school, or with others e.g. In a band?
Playing instruments like guitar and piano can be a bit lonely sometimes - my DC improved enormously once they were playing in music groups.
Also it's really good to have music goals. Sometimes it's exams e.g. grade 1 next March, but it could also be something as simple as playing a Christmas song to Granny on Christmas Day. My niece plays keyboard, and my SIL and I always arrange for the cousins to do a mini concert to grandparents, which everyone actually loves!
Sorry, a bit of a ramble, but hope it helps.
DS nearly gave up the trumpet a year ago over exactly the same sort of 'if you won't practice' argument. That's when we stated the tokens. He kept going and joined a jazz band in his new senior school. In October he played a solo ina school concert, and afterwards was buzzing, and said, 'Mum, I'm so glad you didn't let me give up trumpet'. It was lovely parenting moment!
good luck!