Database

[{"additionalReminders":[["1","1"],[],[],["1"],[],["1"],[],["1"],[],["1"],[],[],["1"]]}]

Query

db.collection.aggregate([{"$unwind":"$additionalReminders"},{"$unwind":"$additionalReminders"},{$group:{_id:null,"additionalReminders":{$sum:{"$toInt":"$additionalReminders"}}}},{$project:{_id:false,additionalReminders:true}}])

Result