Even if there's a severe mismatch with losses of 10 or even 20 dB that won't reduce your ability to hear AM broadcasts. Turn up the volume to offset that.
At any rate, the actual antenna impedance is not very critical
Severe mismatches might reduce the OP's ability to hear weak AM stations or the DX he wants!
Also, overloading can cause desensitizing of the radio and static discharges can damage it. These are common problems with portable radios and long wire antennas.
Use of a loop antenna is usually a good compromise.
Best of luck