For the rest of us not working at LinkedIn I can wholeheartedly recommend the following to prevent burnout:
Don't use social media (like LinkedIn) for a week.
Don't use social media (like LinkedIn) for a week.
The only contact I get now, is not around job opportunities, but people wanting to sell me some product or service 'hey, let's have a 5 minute call to talk about how our companies can help accelerate growth in exciting new ways, let me know when you're available. Let's talk!'.