I Accidentally Broke A Mirror In The Apartment Gym, And Management Wants Me To Pay ~$10,000

I am a grad student in Los Angeles. I was arranging the dumbbells on a rack, and while doing so, I dropped one dumbbell too close to the mirror, which bounced off the floor and hit the mirror. The apartment management said I would have to reimburse $9,255 for it. They recommended that I contact my renter's insurance, which I did, but they said they do not cover the damages I caused in the fitness centre.

I don't have this kind of money. I am a grad student living on a stipend. If I have to pay for this, I would need to take out a loan or something.

What should I do?

I plan on talking with them in person next week, saying it was an honest mistake and I am a grad student, etc., and asking if they can waive this.

The single mirror panel which I broke is about 10 feet x 4 feet, and I made about 1.5 feet x 0.75 feet cracks on the bottom left corner of it.

Edit:

This is the mirror in question. Green is the single panel of mirror, and red is the damage I caused. There is one more dumbbell rack on the left, where I was rearranging some dumbbells and dropped one on the ground, and it bounced and hit the mirror on the bottom.