To solve this expression, we first need to simplify within the parentheses and then perform the subtraction and addition in the correct order.

Given: -2/9 + (2/9 - 3/4) * 4/7 - (5/11 - 3/7)

Simplify within the first set of parentheses:
2/9 - 3/4 = 8/36 - 27/36 = -19/36

Simplify within the second set of parentheses:
5/11 - 3/7 = 35/77 - 33/77 = 2/77

Now we have: -2/9 + (-19/36) * 4/7 - (2/77)

Perform the multiplication inside the first set of parentheses:
(-19/36) * 4/7 = -76/252 = -19/63

Now we have: -2/9 + (-19/63) - 2/77

Find a common denominator for the fractions:
-2/9 = -154/693, -19/63 = -133/693, -2/77 = -126/693

-154/693 + (-133/693) - 126/693
= -413/693

Therefore, the final answer is -413/693.