Synchronization of two audio tracks via Mel-frequency cepstral coefficients (MFCCs)
I think, you do not need to follow complicated steps of MFCC. I recommend you to preprocess the signal. So you can remain the portion between 300~4000Hz. (1. FFT, 2. assign zeros for the frequencies for smaller than 300 and larger than 4000Hz. 3. IFFT) And then you can do cross-correlation stuffs like what you did. Hope it helps.
You can understand the idea of MFCC from here. 

Then you will understand why I don't recommend you MFCC but to remain 300~4000Hz.