11 and 13

Algebra Level 3

$A = \dfrac{11}{13}+\dfrac{1111}{1313}+\dfrac{111111}{131313}+\dots+\dfrac{\overbrace{1111\dots1111}^{\text{Number of 11}=13}}{\underbrace{1313\dots1313}_{\text{Number of 13}=13}}$

Find the value of $A$ .