Nami yo Kiitekure

On a night out drinking to get over being duped and ditched by her last boyfriend, Koda Minare ends up providing a massive drunken rant—while blackout drunk—for Matou, the director of a radio station. The next day, she is shocked to hear her own voice being broadcast on the radio! She rushes to the studio, leaving her job at a curry soup and bread restaurant in jeopardy. However, her drunken rant and the next day's impromptu damage-control live broadcast end up earning her an invitation to try working at the radio station!

(Source: MangaHelpers)