Triangle A_{1} B_{1} C_{1} is an equilateral triangle with sidelength 1. For each n>1, we construct triangle A_{n} B_{n} C_{n} from A_{n-1} B_{n-1} C_{n-1} according to the following rule: A_{n}, B_{n}, C_{n} are points on segments A_{n-1} B_{n-1}, B_{n-1} C_{n-1}, C_{n-1} A_{n-1} respectively, and satisfy the following:
\frac{A_{n-1} A_{n}}{A_{n} B_{n-1}}=\frac{B_{n-1} B_{n}}{B_{n} C_{n-1}}=\frac{C_{n-1} C_{n}}{C_{n} A_{n-1}}=\frac{1}{n-1}
So for example, A_{2} B_{2} C_{2} is formed by taking the midpoints of the sides of A_{1} B_{1} C_{1}. Now, we can write \frac{\left|A_{5} B_{5} C_{5}\right|}{\left|A_{1} B_{1} C_{1}\right|}=\frac{m}{n} where m, n are relatively prime positive integers. Find m+n. (For a triangle \triangle A B C,|A B C| denotes its area.)