I think the t test is appropriate. And I can see clearly that the results, in advance, is significantly different as the -ve values so larger than +ve.
All I can surmise, given what you've said thus far is that, descriptively:
+ve increases across observations. Since +/- ve sum to 60, -ve decreases across observations. (When you have two consitutent elements with a fixed total, they will be inversely related.)
In order to give a better answer to your query, please elaborate by addressing:
1. What question(s) are you trying to answer from your data?
2. What do your counts represent? (What was the sample, the variables, and classification?)