Just as I promised, here's the fix:
: According to n0rthstar, this method does NOT
work with non- intel graphics chips.
1. Download and install DTD Calculator from : clever technologies - products - clever freeware - Home to DTDCalculator
2. Start DTD Calculator and fill in the values on the left side as shown in the attachment.
3. After filling up the values, go to the Registry hack tab. There, click on More to add a row and then in the newly added row, click on Get Calculated.
4. The Registry Hack screen should have DTD1 as the calculated value. Now, click on Write DTDs to registry and reboot when prompted.
5. After you reboot, go to your favorite location of changing resolutions and you should have 1366x768 @ 60 Hz as an option and you can safely switch to it.
A few notes though:
a) I have tried this with Acer X193HQ which has native resolution of 1366x768. You will have to modify the left side values that I have filled in DTD calculator for getting 1360x768.
b) If you do modify the parameters on the right hand side, please do so at your own risk. I can't guarantee that they will be correct for your monitor and there is a chance that you may spoil your monitor.
Really hope this helps!