This sounds like poor compaction.
A good pond builder, especially an 11 foot tall dam, builds the dam in lifts. They'll excavate to hard pan, either thick clay or bedrock on which to use as a foundation. Then, they go up, in six inch lifts, compacting each lift tightly. Bulldozers can't compact. Sheepsfoot rollers, steam rollers and heavy, rubber-tired pan scrapers can compact.
It's not unusual for a lift or two to be improperly compacted, especially if the operator is inexperienced.
If that's what happened to you, the source needs to be identified. That source isn't necessarily where the water flows out. Water seeks the path of least resistance.
Since you describe the dam as 11 feet high and was dug 11 feet deep, to me that means your total depth is 22 feet. If the pond drops 11 feet, which is the bottom of the dam, that suggests the dam wasn't cored properly.
If my assumption is true, digging a core trench along the inside slope of the dam and properly backfilling and compacting it with a trench compactor with solve that problem.
