Yes, my 13600k ran 5600mhz cl36 ram overclocked to 6400 cl30 though I had to turn voltages up. You could get a kit thats already clocked to 6000 or more and just turn on xmp to make it easy. It should run, even 7000. But the higher you go the more risk of instability there is. But just 6000? Yeah that should be no problem.
Yes, my 13600k ran 5600mhz cl36 ram overclocked to 6400 cl30 though I had to turn voltages up. You could get a kit thats already clocked to 6000 or more and just turn on xmp to make it easy. It should run, even 7000. But the higher you go the more risk of instability there is. But just 6000? Yeah that should be no problem.