Prove GCD(6n + 1, 6n + 5) = 1 for all integers n

[voyage200]

I having trouble proving that 6n + 1 and 6n + 5 are relatively prime for all integers n.

This is what I got so far:

Let d = GCD(6n + 1, 6n + 5), so:

. . .d|6n + 1
. . .d|6n + 5

Then I can write as:

. . .d = (6n + 1)x + (6n + 5)y

But I don't know how I would prove that GCD(6n + 1, 6n + 5) = 1