Let $$𝐴𝐵𝐶𝐷$$ be a rectangle and let $$𝑀, 𝑁$$ be points lying on sides $$𝐴𝐵$$ and $$𝐵𝐶$$, respectively. Assume that $$𝑀𝐶 = 𝐶𝐷$$ and $$𝑀𝐷 = 𝑀𝑁$$, and that points $$𝐶, 𝐷, 𝑀, 𝑁$$ lie on a circle. If $$(AB/BC)^{2} = m/n$$ where $$m$$ and $$n$$ are positive integers with $$gcd(𝑚, 𝑛) = 1$$, what is the value of $$𝑚 + 𝑛$$?