In high school like twenty years ago, we actually did a simple experiment demonstrating sound cancellation like this with simply speakers facing each other with polarity reversed. That surprisingly works well enough to definitely notice it working, when you are positioned in the right place, which is pretty cool.
It also works well enough to see it doesn't really do what you are describing. The energy from negative copy sound waves is being used to cancel out the original sound waves, the better it's working the less energy there is going to sound waves "escaping" to be heard anywhere else.
If the two speakers were any closer to each other than say 80 feet or 25m (which is roughly how far sound travels in 0.1 second), I wouldn't expect you to have heard the effect I'm describing. There would have to be enough distance between the "source" and the "canceller" to throw off the timing.
It also works well enough to see it doesn't really do what you are describing. The energy from negative copy sound waves is being used to cancel out the original sound waves, the better it's working the less energy there is going to sound waves "escaping" to be heard anywhere else.