fake proofs - Can this really happen?

Yesterday, while scribbling on the back page of my maths copy, I accidentally came across this

If $x\in R\ $ and $x+x+x+.....\infty = m$ where $m$ is any real number.

Then we can write

$x+x+x+.....\infty = m$

$\Rightarrow$ $x+m=m$

$\Rightarrow$ $x=0$

In the same way we can prove that $6=0$ or $7=0$

But how is this really possible? Please explain. I am in 10th standard.