gcd(m,n) and modular arithmetic

"If gcd(m,n) = 1, show that for any pair of integers a and b there exists an integer x such that x ≡ a mod m and x ≡ b mod n."

I'm having trouble interpreting this problem. When I look at this, I think, for example:

m = 7
n = 11
a = 6
b = 8

and

x ≡ 6 mod 7 -> 6
x ≡ 8 mod 11 -> 8

I'm not sure what I'm doing wrong. If someone could show me an example of integers m, n, a, b where the problem works I think I can finish the problem. Any response is appreciated.

>>1
"x ≡ a mod m" is a weird notation. It does NOT mean that x is equivalent to the modulo operator applied to a and m. Instead, it means that the equivalence "x ≡ a" holds if we consider both x and a modulo m. In effect, it means that "modulus(x, m) ≡ modulus(a, m)". You're interpreting it as "x ≡ modulus(a, m)".