Near Equal

Tsubaki is her school's most proficient student, being polite and is absolutely good at everything and little by little people are hailing her to be the school's queen.... And she absolutely despises that. She quietly admits to herself that being a "perfect student" is not her real personality, but a clever ruse to become a more likable person.
She is, however, still not able to interact normally with students and thus is dissatisfied; fact that prompts her to follow the advice of a magazine on finding happiness; the magazine states that by meeting your doppelganger, you will achieve long-lasting happiness. Determined, Tsubaki follows the instructions in the magazine and opens up a door that will allow her to meet her doppelganger....
... And who she meets at the other side of the world is not who she was expecting.... well, it is someone who is strangely identical to her when it comes down to it, but it is also essentially different.