When \left(3+2 x+x^{2}\right)\left(1+m x+m^{2} x^{2}\right) is expanded and fully simplified, the coefficient of x^{2} is equal to 1 . What is the sum of all possible values of m ?
Answer Choices
A. -\frac{4}{3}
B. -\frac{2}{3}
C. 0
D. \frac{2}{3}
E. \frac{4}{3}