Marcin, as you have alluded to, an antenna is resonant when there is no reactance present in the impedance seen at the feed point for the frequency you are using. There is no reactance because at resonance the antenna voltage and current are in phase, not because the inductive and capacitive reactances cancel out. When the antenna is not resonant, the voltage and current are not in phase which results in the impedance containing some reactance.
Assuming you are not changing the antenna or it's feed point and you are changing the frequency, the frequency at which the impedance has the lowest resistance (ignoring if there is any reactance present) does not however always match up with resonance.
The value of the resistive or real part of the impedance does not determine whether or not the antenna is resonant. At resonance there is no reactance, not least resistance.