In a medium bowl, combine the chicken with 2 1/2 teaspoons of white sugar, 1 1/2 tablespoons vinegar, and 1/4 cup soy sauce. Mix well to coat the chicken. Cover and marinate in the refrigerator for at least 1 hour.

In another medium bowl, combine chicken broth, water, sesame oil, ground black pepper, remaining sugar, vinegar, and soy sauce. In a separate small bowl, dissolve cornstarch in a little bit of this mixture, then add it slowly to the rest of the mixture, stirring well. Set aside.

Cook linguine according to package directions, drain, and set aside.

Heat 1 tablespoon of vegetable oil in a wok or large saucepan over high heat until smoking. Add the marinated chicken and stir-fry for 4 to 5 minutes, or until browned. Transfer chicken and juices to a warm plate.

Heat the remaining vegetable oil in the wok or pan over high heat. Add ginger, garlic, mushrooms, and green onions, and stir-fry for 30 seconds.

Add the reserved sauce mixture and then the chicken. Simmer until the sauce begins to thicken, about 2 minutes.

Add the reserved noodles and toss gently, coating everything well with the sauce.