fyi- neither of these sentences would be used in American English. You must apply by July 11. A "closing date" typically relates to the signing of a (complicated) contract. We wouldn't use it to indicate the last day you could apply for something.

yes the 11th, but what hour of the 11th?

Yes, if the closing date is 11th July then applications received on 11th July are accepted, but any received on the 12th are too late. So applications must be received before 12th July is true.