Studying English will not only help students improve their networking skills but also increase the chances of getting a job.
or
Studying English not only will help students improve their networking skills but also increase the chances of getting a job.
Either would be understood. I would go with the first, however because the verb form is better in parallel: will not only help ... "
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Either would be understood. I would go with the first, however because the verb form is better in parallel: will not only help ... but also increase..."
By the way, I would say "increase their chances" to match "improve their ...skills."