1. **State the problem:** We are asked to find the result of adding the two equations: $$\begin{aligned} -2x + 7y &= -5 \\ -2x - 4y &= 6 \end{aligned}$$ 2. **Add the left-hand sides and right-hand sides separately:** $$(-2x + 7y) + (-2x - 4y) = -5 + 6$$ 3. **Combine like terms on the left:** $$-2x - 2x + 7y - 4y = 1$$ 4. **Simplify the expression:** $$-4x + 3y = 1$$ 5. **Final answer:** The result of adding the two equations is $$\boxed{-4x + 3y = 1}$$