Вот один из способов сделать это:
import collections
data = [[[1,11], [1, 10], [2, 20], [2,15], [2, 100], [3, 56]]]
# why not data = [[1,11], [1, 10], [2, 20], [2,15], [2, 100], [3, 56]] ???
sums = collections.defaultdict(int)
for k, v in data[0]: # data[0] because data is in strange format
sums[k] += v