English Translation
Tom will get married to Mary next week.
I believe this sentence works, especially in casual conversation, it might be colloquial. But to be precise and unambiguous using “επόμενη” instead of “άλλη” would make it clearer that something is happening the next week. την άλλη seems to be more open and could mean ‘another week’ (not this week) - it’d be nice to have a native speaker explain this one.