Consider the set of complex numbers z satisfying \left|1+z+z^{2}\right|=4. The maximum value of the imaginary part of z can be written in the form \dfrac{\sqrt{m}}{n}, where m and n are relatively prime positive integers. What is m+n?

**Answer Choices**

A. 20

B. 21

C. 22

D. 23

E. 24