When you look at the oemlasersystems.com website for goggles->specifications, you see a transmission curve (actually the negative decadic logarithm of the transmission). The higher the line above the x-axis, the better the protection.
One of the best (and most expensive) models for hobbyists is the ML7. You can see from the curve that it blocks blurays at 405nm essentially completely (OD>6 i.e. reduction factor 1:1 Million), that it blocks DPSS green at 532nm (Peak reaching up to OD 3 = 1:1000), and that IR above 800nm is also very well blocked (1:10000). So, how about red? A 635nm orange-red is blocked by a factor of 30 or better (OD>1.5). These tend to be low-power, so it's ok. And your 300mW LPC-815 burner at 660nm (or possibly a bit more)? Well, it's just outside the range, you can expect a protection of about OD 1..1.5 for that one, so effectively the power is reduced to 10..30mW. Not good, but you have a real chance to blink and look away before you're getting permanent eye damage.
So, a statement like "these goggles will protect from 630-650nm" misses a vital information: what exactly does "protect" mean? What is the minimum optical density (OD) in that region? If it's 1.0, don't count on them to help you at 660nm. If it's 1.5, they may make a crucial difference, but aren't optimal. If it's 2.0, then they will most likely be good enough at 660nm (it depens on how steep the curve is, but generally the cheaper the goggles, the shallower the hills and valleys are going to be).