194815

First I made cards from 1-15, and started to make some combinations in a systematic way. I found out that there are only 2 because otherwise you would need numbers over 15 or use a number more than once. For example: if you used 10 and 5, you would need to use 8 twice to make 15. My solutions were:
6+9+11+12+4+14+7 and 8+7+13+10+6+12+9.