CZ-SK-MO 2014 Problem 1

Let be $n$ a positive integer. Denote all its (positive) divisors as $1=d_1<d_2<\cdots<d_{k-1}<d_k=n$ . Find all values of $n$ satisfying $d_5-d_3=50$ and $11d_5+8d_7=3n$ .

(Day 1, 1st problem author: Matúš Harminc)