Synchronous Motor Power and Frequency Relationships
The current that is due to the mechanical load will increase if the mechanical power also increases. Given that increasing the frequency also proportionately increases the speed (and more-than-likely also increases the torque to the mechanical load), it is likely that a 6:5 increase in speed delivers a 36:25 increase in mechanical power hence, for a given supply voltage, the current (due to load) will rise by 1.44 times.

Also remember that there is magnetization current into the stator and this will decrease with an increase in frequency (voltage remains constant) so, the net effect will be somewhat less than a 1.44 times increase in overall current but somewhat more than simple a 6:5 (1.2 times) increase in current.