Full Moon Wo Sagashite

Full Moon focuses on a 12-year-old girl named Mitsuki Kouyama. Mitsuki is a talented singer who dreams of becoming a pop idol, but she is afflicted by throat cancer, which is curable only through a surgery that will require the removal of her vocal cords. At the beginning of the series, she is visited by two shinigami whom only she can see, Takuto and Meroko, who go by the team name "Negi Ramen" or "Spring Onion Noodles" ("Green Onion Ramen" in the English dub). These shinigami accidentally tell her she has but one year left to live. Mitsuki realizes she cannot wait any longer and attempts to achieve her dream of becoming a singer. However, she does not look old enough to be a singer, so she makes a deal with one of the shinigami, Takuto, to transform her into a 16-year-old. In her 16-year-old form, her throat is healthy, and she is able to sing without any difficulty. She uses the stage name "Full Moon" to hide her identity from the public. To start a career as a singer, 16-year-old Mitsuki auditions in a singing contest. Though there is much competition, she is able to win over the judges with her enthusiasm for singing and her excellent voice.

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Note: This is an Anime, not a cartoon.