Exponents these days! :/

Algebra Level 2

Enter the sum of \[A=\frac{1}{1+x^{b-c}+x^{b-a}}+\frac{1}{1+x^{c-a}+x^{c-b}}+\frac{1}{1+x^{a-b}+x^{a-c}}\] and \[B=\left(\frac{x^{m}}{x^{n}}\right)^{m^{2}+mn+n^{2}}\times\left(\frac{x^{n}}{x^{l}}\right)^{n^{2}+nl+l^{2}}\times\left(\frac{x^{l}}{x^{m}}\right)^{l^{2}+lm+m^{2}}\]