I'm 5' 10.75" and have ridden 56 and 57 road frames since I was young. That size, more specifically 57cm measured C-T, just fits me.

You're a few inches taller which would move you to 59 or 61. You're about 3.25 inches taller which is split front and back, so (3.25 X 2.54) / 2 = 4cm. So 56 + 4 = 60, 57 + 4 = 61. Depending on your comfort at the bars, you could fit a 59 or a 61. It is my opinion that it would be better to choose the smaller of the two frames and use seat and stem adjustments to sort out the final fit. A larger than required frame adds weight unnecessarily and frame flex.