Is there a difference between a 'mini-DisplayPort to HDMI cable' and a 'mini-DisplayPort to DisplayPort' cable for a MacBook Pro?
Officially, your model MacBook Pro will support up to 3840 by 2160 pixels at 30Hz or 4096 by 2160 pixels at 24Hz if using a HDMI connection, which explains your experience of 30Hz with your mini-DisplayPort to HDMI cable.

Your model MacBook Pro also supports up to 3840 by 2160 pixels at 60Hz using a Thunderbolt connection. Since your display supports both a 60Hz refresh rate and a DisplayPort connection, then using a mini-DisplayPort to DisplayPort cable of sufficient quality should achieve what you want.