It’s hard to say without knowing your full convention card in relation to opening bids, but I have no issue with 1C.
2C in standard precision means a club opener 11-15 6 clubs. So that’s out, you have diamonds. If this were 2/1 standard then it’s okay to open this 2C probably depending on the other options.
3NT is not a good idea - you don’t actually have the correct hand for that technically (requires AKQ) though it’s probably fine from a realistic standpoint there - but it also requires nothing outside. That pesky A of spades means it’s a no. If you DO have a slam odds are your partner passes!
Quick tricks are often used to evaluate freak hands - this one has eleven, so it clearly is okay to bid as if it were ‘strong’. I wish it had the Qd - that would mean diamonds was definitely no losers - but it’s still safe to say it’s probably going to fall out.
The bigger problem is how do you get the info you need? You need to set up an exchange where you can game force and then get into asking for controls. Don’t worry as much about points - worry about getting to that control asking spot. Precision club usually makes that pretty easy.
Edit: After talking this over with my expert friend, there's another option that I didn't mention. Open 6D (or, perhaps, 5D)! You have 11 tricks in hand; opening 6D is not entirely crazy, given that, just hoping partner has one, and it's highly unlikely you'll find out about the card(s) you need. 5D is a bit different, in particular as often that's considered weaker - not to make - and so it's less likely that you get to slam; but it's possible you end up at 5DXX which can score a rather large number of points itself. Taking out opponents' room to discover their fit (hearts, as it turns out, but given your hand it could be any suit really) is very helpful here as it's less likely they can mention it at the 5 (or, obviously, 6 level).
This of course begs the question - if you have the listed hand in the problem, do you raise 6D?