I would suggest rephrasing the sentence to be more polite and specific. Here's an example: "I was wondering if it would be possible to receive an invitation from Alex for the eleventh of April. If it's not too much trouble, could you please let me know as soon as possible?"
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I hope to receive an invitation from Alex soon for the eleventh of April/April 11/11 April.
I wasn't completely sure what your intended meaning was, so I interpreted it as well as I could. As for "April 11" versus "11 April", it just depends on which country you are in. But of course you can say "the eleventh of April".