Hello sangrampp,
I have developed business applications using CakePHP for my former employers, and have interfaced Facebook for a client of mine too. Been in the industry for two decades and have evolved and adapted to the different technologies and their implementations. I guess my question would be what version of CakePHP have you used.
Admittedly, I have not implemented Linkedin yet, but given the trends with Google, Facebook and Twitter, and my experiences in using various APIs in the corporate world, I am confident this would not be a hindrance.
Please do contact me should you be interested.
Regards,