There is no difference in the use of "aim" instead of "objective" in your context, however, the right preposition for enroll is "in" . You need to drop"the" as well. Therefore, your sentence should read; My objective is to enroll in MIT.
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But you can find a lot of the usage of "enroll at MIT" on the internet. How should I interpret the fact?
the right preposition for enroll is "in