Another tricky 700 level problem

First, let's calculate x,y,z to find out m, n
4+x = 1 ==> x=-3
4+y = -5 ==> y=-9

Let's hold on z as of now, because we don't know what m is. Now focus on 2nd row to find out e and n,
We now know that x equals -3,
e+x = 7 ==> e-3 = 7 ==> e=10

Now calculate n using e and y,
e+y = n ==> 10-9 = n ==> n=1

Now, find out z using e,
e+z = 10 ==> 10+z = 10 ==> z=0


Finally, calculate m using z,
4+z = m ==> 4+0 = m ==> m=4

Now we have found m and n values, calculate m+n
4+1 = 5

Answer is 5.