Algebra or Number Theory?

Given that

$m^2+2(3^n)=m(2^{n+1}-1)$

has nonnegative integer solutions $$(m_1,n_1),(m_2,n_2),(m_3,n_3),\ldots,(m_i,n_i)$$, find the value of

$(m_1+m_2+m_3+\ldots+m_i)+(n_1+n_2+n_3+\ldots+n_i).$

Details and Assumptions

This problem is not entirely original.

×