How to earn back my daughter's trust?

Monday was my daughter's 6th birthday and i promised her i would be there. The night before i got drunk at a party and had such a horrible hangover i forgot it was her birthday and didn't show. My EX Wife Stacy was furious on the telling me she was crying and feeling lied to since i promised to be there. I never felt worse in my life i decided to go into AA to try and get my life on track. I feel like i have lost her trust and i will do anything to get it back. My daughter is my whole world she means everything to me. How do i earn her trust back?