has anyone successfully hooked back up with their ex and are happy together now?

My girlfriend broke up with me a month ago and it's slowly taking a toll on me mentally. I would do anything to get her back. Anyways has anyone successfully hooked back up with their ex and how long did it take you to do so and how happy are y'all now? Bonus: Do you think writing a letter to my ex explaining how I realized my mistakes in the relationship and how much she means to me could help me get her back? her reason for breaking up with me was because she didnt feel the same anymore after two years of being in a relationship . If not any advice you can give me? Thanks