Single Pilot reported a critical ground conflict during take-off roll with opposite direction take-off aircraft passed overhead. Single pilot contacted the conflict aircraft who stated they did not hear any departure calls.

Narrative

I was holding short for Runway XX. The winds were calm and an Aircraft Y was landing opposite direction on [Runway] X. ZZZ [Center] cleared me for release; but since Aircraft Y was on a 5 mile final; I told Aircraft Y I would wait until we landed. I also gave this information to ZZZ Center. He acknowledged my call; landed then cleared the runway. Aircraft Y thanked me for waiting; then I made a call on Unicom that I was taking [Runway] XX to depart to the east.I did not hear any other calls; but I knew I was on Unicom because Aircraft Y and I communicated and coordinated our departure. During my take-off roll; I saw a plane coming towards me on Runway X. I was at Vr; but held the plane on the ground until the plane went overhead. I was going too fast to abort; so I took-off after the other plane was past me and headed east.I communicated on Unicom that I was departing the area when the other plane; Aircraft Z; said he announced he was taking Runway X; but didn't hear my call. I think he either missed his call or was on the wrong frequency. When the wind is calm at ZZZ; planes will use both directions; usually based on direction of flight. In fact; a plane was on the RNAV to [Runway] XX when I took-off on XX because I heard them on ZZZ Center when I was released.