To solve this expression, we need to find a common denominator for all the fractions. The common denominator for 5, 11, and 10 is 110.

Now, let's convert each fraction to have a denominator of 110:

-2/5 = -22/110
7/11 = 70/110
-11/10 = -121/110
7/-11 = -70/110

Now, we can add the fractions:

-22/110 + 70/110 - 121/110 - 70/110

Combining the numerators:

(-22 + 70 - 121 - 70)/110

Simplifying the numerator:

-143/110

Therefore, -2/5 + 7/11 - 11/10 + 7/-11 = -143/110.