The short answer is, you might or might not be able to.
Coinless or TITO (ticket-in ticket-out) machines, as they're known, all issue tickets with expiration dates, although the length of their validity varies from property to property. Thirty days is the minimum, while 60 days is more common. Occasionally, you might come across a ticket that's valid for 90 days, but that's unusual.
In reality, the stated expiration date is somewhat moot. Most casinos are happy to cash an expired ticket, pretty much regardless of how old it is, although the further past its expiration date and/or the higher the amount, the further up the personnel chain they'll need to go to honor it. If you have a ticket that's old, it won't be accepted by a machine, but take it to the cage and if the cashier can't approve it immediately, she'll call a supervisor who will.
So, it you’re planning a trip back to Las Vegas sometime in the not-too-distant future, you can bring the ticket with you, go to the issuing casino, and go through the process.
If not …
Unlike winning race and sports tickets, most slot receipts must be presented in person. If you know someone in Vegas that you trust, you can send it to him or her to handle the transaction.
If not …
Some casinos will accept TITO vouchers mailed in. Definitely call the casino in question, ask for the slot department, and see what they tell you. If you can mail in your ticket, it’s recommended that you keep a photocopy of it and mail it certified or registered. Of course, you’ll have to subtract that cost from the $76, but anything you can get back is better than nothing.