You need to get a proper invitation letter from the academy, i.e., the academy needs to state the purpose of your trip in the letter, and it also needs to explicitly state in the letter that the academy will provide accommodation and food.

Again: this needs to be stated BY THE ACADEMY and IN THEIR LETTER. That you claim in your letter that this is true is irrelevant for the visa - the institution providing the support needs to make these statements.

Get them to write the letter and fedex or fax it to you as quickly as possible. Then try to get an expedited visa through one of the visa service agencies, if this is available in your country (if you had stated where you come from it would have been easier to help...).