I know that there exist some attack when using same modulus.
Can two different pairs of RSA key have the same modulus?
RSA cracking: The same message is sent to two different people problem
But with a little modification,
$m$ is the plain-text
$N$ is the RSA modulus
$r_1, r_2$ is the random padding
$e, s$ is the public exponent
$C_e, C_s$ is the cipher-text
encrypt as follow $$С_e = (m + r_1)^e \bmod N$$ $$С_s = (m + r_2)^s \bmod N$$
If attacker only knows $C_e, C_s, r_1, r_2, e, s, N$.
Is it possible to know $m$?
It seems the RSA cracking: The same message is sent to two different people problem does not work?