In a medium, non-reactive bowl, combine the chicken with 2 1/2 teaspoons of white sugar, 1 1/2 tablespoons vinegar and 1/4 cup soy sauce. Mix this together and coat the chicken well. Cover and let marinate in the refrigerator for at least 1 hour.
In another medium bowl, combine the chicken broth, water, sesame oil and ground black pepper with the remaining sugar, vinegar and soy sauce. In a separate small bowl, dissolve the cornstarch with some of this mixture and slowly add to the bulk of the mixture, stirring well. Set aside.
Cook the linguine according to package directions, drain and set aside. Heat 1 tablespoon of the vegetable oil in a wok or large saucepan over high heat until it starts to smoke. Add the chicken and stir-fry for 4 to 5 minutes, or until browned. Transfer this and all juices to a warm plate.
Heat the remaining vegetable oil in the wok or pan over high heat. Add the 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.