It's described in manual ch 34.6.
See there especially the diagram about advanced balanced phone mode.
On the right hand side of the drawing it's clearly visible that phones outputs 1/2 and 3/4 (TRS) have to be used, where T and R are being used.
You would need a cable
Ph 1/2 - TRS -‐---------------- Mini TRS R
Ph 3/4 - TRS ------------------ Mini TRS L
My recommendation to you:
As your normal stereo cable has a symmetric layout to the left and right side of your phone and the impedance of your phones does not really require a higher volume, you can IMHO save the effort to purchase a special cable separately with that layout which might be expensive.
I doubt that you would hear any difference between balanced and non balanced mode at same listening levels. This topic has been discussed a few time already. Confusion usually arises when people A/B tests because they forget to compare at exactly the same listening levels and in balanced mode the volume is if I remember right 6dB higher and our ears / brain regards louder as sounding better. On top come other psychoacoustic effects, the expectation that balanced sounds better and this you can usually fully exclude as a blind d test would require a double setup and in a sighted test you can't fully exclude your expectations.
Other aspects
SNR is already on such a high level in unbalanced mode that this is inaudible and if you hear no noise, then you have no problem with noise. A few dB higher SNR will not make the sound better, it will only make "more inaudible" as it already is in unbalanced mode.
Same story with my Audeze LCD-3. It also has a symmetric wiring beginning from the TRS plug in e.g. phones 3/4 up to each of the two drivers. I also use the normal good cables, get an excellent sound and do not need to spend another €300-500 for special cables which have their price tag because balanced cables are "special" and not so often being sold.
I would simply enjoy the ADI-2 Pro and your headphones in unbalanced mode.
BTW the balanced cable that comes with your phones would be much to short for me anyway with only 1.2m. This is way too short and doesn't allow for a flexible placement for listening. The normal cable has nice 3m, that's fine. My recommendation, simply use that and all will be fine.
If you feel better with a balanced cable please do and go ahead. I only wanted to tell you that it is not really needed.
BR Ramses - UFX III, 12Mic, XTC, ADI-2 Pro FS R BE, RayDAT, X10SRi-F, E5-1680v4, Win10Pro22H2, Cub13