Coming from US - no problem whatsoever with 60 minutes as long as you're not on a habitually late flight (check flight history for your flight on flightradar24).

Coming from BKK/SIN/ICN/etc.. 60 minutes is cutting it close. I've made it on separate tickets where I was checked through, but it was tight, and my arriving plane was only 5 minutes or so late. It took me 25 minutes to get through bag security and I was the first person off the plane. That said, if your originating airline checks you through, they'll know about you and hold the plane up (which they did on my flight that was tight). It only works if you don't have to get a boarding pass AND you have no flight issues coming in. There's no room for error.