Cook rice according to package directions, omitting salt and fat.
Combine chicken and next 3 ingredients in a bowl; toss to coat. Heat a large skillet over medium-high heat. Add canola oil and sesame oil. Add chicken mixture and saute for 4 minutes or until lightly browned. Increase heat to high, and add broccoli and the next 4 ingredients (through red bell pepper). Cook 5 minutes or until vegetables are crisp-tender and chicken is done, stirring frequently. Stir in cashews.
Combine vinegar and remaining ingredients in a small bowl; stir with a whisk. Add vinegar mixture to chicken mixture; toss to coat. Serve with rice.