Determine the smallest possible positive integer P which is not a perfect seventh power, but in the decimal expansion of its seventh root, the decimal point is followed by at least ten consecutive zeroes.

At the outset, I wish to acknowledge the outstanding analytical reasoning employed by Tristan in solving this problem. Although, I had arrived at the same solution, that is P=52523350145, it was only with the synergy of mathematical methodologies and analytical reasoning inclusive in his response that has allowed me to post a comprehensive solution to the problem under reference. <o:p></o:p>