Consider the following:
a. Primary Website, ex. primary.com (just like this one), outlining your general offer with an entry way signup for mentors and an entry way sign up for mentees.
Work on your overall SEO for this specific site as general SEO for the niche that you are operating in.
b. primary.com/landing-page-mentors - use this page as your fishing hook for mentors and optimize this page. You want it to remain on the primary domain, because you need to build domain authority, as well as page authority.
c. primary.com/landingpage-mentees - same as above, but targeting your mentees
You'll also want to use an opt-in email pop-over or page takeover with your landing pages to harvest email addresses. You should have three lists in your MailChimp or equivalent account. Your primary, your secondary for mentors, and your secondary for mentees. When the target is on the specific landing page, you want to serve them the correct pop-over or page takeover. Or, you could have it in the sidebar, as well. That way, you're list building and able to market and offer coupons to mentees, as well as provide valuable thought leadership collateral to mentors who want to follow you.
You want an overall SEO and marketing campaign for your marketing site, but you can really be strategic with your landing pages, which drive interest to action. It's a combination of SEO, then offering mentors a carrot to opt-in to be a mentor and mentees a carrot to opt-in to be mentored.
That's why we have single page, scrollable landing pages now. So that you can target each landing page to a specific audience.
Of course, DO NOT put duplicate content from a. on b. or c., because that will get your site penalized.
If you are using WordPress, my company, Digital Strategy Works, can help you achieve your goals with site layout, design, and implementation, as well as landing page optimization and SEO. I am also the Community Manager for All in One SEO Pack for WordPress, the most downloaded SEO plugin and the choice of true SEO professionals. I can certainly help guide your overall strategy, if you need assistance.