An algebra problem by أحمد الحلاق

$\large \left(1 + \dfrac1{1 + 2^1} \right)\left(1 + \dfrac1{1 + 2^2} \right)\left(1 + \dfrac1{1 + 2^3} \right)\cdots \left(1 + \dfrac1{1 + 2^{10}} \right)$

If the expression above can be expressed as $\dfrac mn$ , where $m$ and $n$ are coprime positive integers , find $m+n$ .