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You just didn't have the sack to face those tears.

What does sack here mean? I find a slang explanation of which isn't appropriate to type it down here, but I think you know it. So does it make the dirty meaning here?
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Your sentence means nothing to me.

If the slang expression you are referring to is "You don't have the balls to ...", then it's not 'dirty'. It's not the language one would use in polite circles, but it's quite commonly used informally to mean "You haven't the courage/nerve to ...". I have not heard 'sack' used in that way.
Comments  
Students: We have free audio pronunciation exercises.
The contexts is that a man dumped his girlfriend through the answer machine. So one of his female friend said this sentence to him. I think the meaning of 'courage' here makes sense, however, I just want to know the correct meaning.
What is difference between Proverb & Idiom