In general, I like to take the approach that most of the corals that we keep get spectrum of 5500 to 6500K in nature... some are deeper than this, but not very many. While most hobbyists take the approach to "prove" why corals need more than X spectrum, I like to ask people to "prove" why you should take any of this spectrum away since they did evolve and adapt to take advantage of nearly everything in nature. With every passing year, we are finding that spectrums forsaken in prior LED models are plenty important... it was not long ago that UV was "worthless," yet all now see the virtues. IR is next - IR helps coral move energy from PSII to PSI and process energy and they cannot grow as fast or be as adaptable without it, but they can live. Soon, all fixtures will have IR because of this, or just because everybody else is doing it too and they can sell more panels.
It is a good idea to blue up the spectrum a bit because corals under 5500K are not all that enjoyable to look at, but you can have a very good looking tank with still tons of red, yellow, green and IR. I like a good 14-15K look with crisp white water and lots of pop.
The absolute best looking corals are grown under 6500K bulbs and then are moved to tanks with more blue to show off that color.
Another thing of importance is that it is nearly impossible to blast corals with most white LEDs since they have too much bad spectrum peaks in the diodes - this is why they need kept low since the corals have to use energy to reject/fight-off this spectrum. The same corals can thrive with tons of white light from VHO, T5, MH, etc. that are better quality. ...so when you are taking about white light, the source matters.
If you want the best pop possible, get a few 6500K T5 bulbs and then blast the coral with tons of blue LED or T5 bulbs as well. This can be the best in coloring and illuminating coral. There are some MH bulbs that do this all-in-one... Phoenix 14K in DE and Radium 20K in SE are great at doing this stand-alone.