Consecutive integers

Number Theory Level 4

Let \(a < b < c < d\) be four consecutive positive integers such that

\(a\) is divisible by 5,
\(b\) is divisible by 7,
\(c\) is divisible by 9, and
\(d\) is divisible by 11.

Find the minimum value of \(a+b+c+d.\)