Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain and rinse with cold water.
In large bowl, combine brown sugar, salad dressing, lemon juice, vinegar and salt. Toss dressing mixture with cooked pasta, celery, green pepper, onion and chicken. Chill until ready to serve. Mix in cashews just before serving.