PurpleAngel actually covered a similar question in great detail here:
OP, I just want to check: your issue is that the DX has no dedicated headphone amp?
Because it does have a headphone output. I've used it frequently with my HE-400 (35 ohm, 92.5dB) and DT 880 (250 ohm, 96 dB). Have never gone past 60% of the DX's volume, Windows volume set at max.