Assume that when you changed the frequency from 50 to 60 Hz that you mean the rated frequency but you then ran the motor at the same speed. By doing this you have altered the motor set up calculations that could have changed two items giving a different resistance.
The first is that the slip speed would be different that gives different equivalent rotor resistance values when referred to the stator. The equation is actual rotor resistance / slip. The other is that the skin effect factor at 60 Hz would be higher that increases the resistance of the windings. This is a very significant effect in deep bar rotors.
In an induction motor rotor the copper bars are in laminated steel slots and current only flows in the rotor when current flows in the stator via transformer action. When the motor starts the rotor frequency is high and the flux from the stator does not fully penetrate the rotor steel so it only induces current in the part of the rotor bars near to the air gap. When the motor is near full speed the rotor has very low induced frequencies e.g. 2.5 Hz, so the stator flux fully penetrates the rotor steel and produces current in the total rotor copper.
This is not a change in the rotors DC resistance but a variable coupling factor looking like a varying resistance.
If you look at the complete equivalent circuit of an AC motor you will find an inductance called the "Magnetizing Branch" intended to represent the iron/core losses in the motor. Since the reactance of this inductance is a function of frequency, it goes up as the frequency does. This enables the model to account for the effect of frequency on the inductive elements, just like skin effect accounts for the change in resistance with increasing frequency.
Z = R + jX
By changing the frequency from 50Hz to 60Hz, "Z" will increase due to two factors"
(1) "X" depends on frequency and thus it will increase by increasing F".
(2) "R" doesn't depend on "F", but may increase due to overheating of the wingdings caused by increasing the frequency.
So by altering the slip the rotor resistance appears to change.
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