Pilot reported having a near mid-air conflict with another aircraft that was cleared on the same approach path at the same time.

Narrative

I was flying on an instrument flight plan. I was cleared for the rnav GPS 36 approach to Kearney airport by Minneapolis center frequency 119.4 I was cleared for the approach and given the frequency change before the intersection BLUME. I started the approach high; and I knew I could catch the glideslope on the intermediate segment. The intermediate fix is BELON. About 2 miles north after belon; I Heard another pilot make a position report at BELON and he stated he was shooting the ils 36 approach. Are used the seat have to try to determine his position because it sounded to me like he and I were in the same place and I was IMC and I was cleared for the approach and I was shocked to hear anyone else also on the same approach at the same time since I had received my clearance from Minneapolis center. I asked the other pilot if he had a transponder because I was surprised that Minneapolis center hadn't warned me that there was traffic in the area but I wasn't expecting any traffic because it was I have far at Kearney that morning. When I started the approach it was 600 broken.